the object to be observed, and the construction is in all other respects identical with the common magic lantern, and the oxy-hydrogen microscope. In the case of the microscope, however, whether illuminated by the sun or the brilliant oxyhydrogen light, great regard must be had to the forms of the lenses and the perfection of the setting; while a comparatively very rough instrument forms a very amusing toy as a magic lantern, exhibiting grotesque figures and scenes, which are painted in transparent colours upon glass slides. The arrangement of the apparatus will be understood from the annexed diagram; r is a reflector for turning the sun's m rays in a direction parallel to the axis of the instrument: c is the lens for concentrating these rays upon the object placed at o, a little further from the first lens, p, of the magnifier, than the focal length of this magnifier, which is one-fourth the focal length of p; then we have p and m, the two lenses forming the magnifier, which are of equal focal length, and separated by an interval equal to two-thirds of the common focal length, as in Ramsden's positive eye-piece: lastly comes the diaphragm, d, placed at a distance from m, the second lens of the magnifier, equal to the focal length of this magnifier, which is one-fourth the focal length of m or p. The best forms of the two lenses are, for the first, a planoconvex, and, for the second, a convex meniscus, the radii of whose surfaces are as 1 to 15; and the advantage aimed at in this construction is to render the image flat, and consequently capable of coinciding with the plane screen upon which it is to be received. A similar purpose is the object of the construction of Ramsden's eye-piece, viz., to obtain, as it is there called, a flat field. The object being placed a little further from p than the focal length of the magnifier, the pencils of rays from each point of the object, after passing through the two lenses, become slightly convergent, and, at a distance from the diaphragm depending upon the distance of the object from the lens p, the magnified image is formed inverted with respect to the object. THE CAMERA OBSCURA. This instrument consists of a plane reflector, upon which pencils of light from the various points of a landscape are received and reflected, so as to pass first through a diaphragm, and then through a plano-convex lens, after which the rays of the pencils become convergent, and form an image upon a screen in a darkened chamber placed to receive it. The diaphragm and lens are placed in a tube, which is passed through a hole in the chamber just large enough to receive it, so that no extraneous light may be admitted. The distance of the lens from the diaphragm is determined upon the condition that the image shall be distinct. The form of the screen also, that the image may be distinct, is a paraboloid of revolution, or figure formed by the revolution round its axis of a parabola, whose radius of curvature at the vertex is f, μ being the refracting power of the medium of which the lens is formed, and f the focal length of the lens. A curved surface of this form is, therefore, made of plaster of Paris, and placed at a distance from the lens rather greater than the focal length, the exact distance depending upon the nearness or remoteness of the landscape to be depicted, and being easily found by trial. If the camera be set up in the neighbourhood of a well-frequented thoroughfare, we have then an agreeable succession of distinct and vividly-coloured pictures, differing from finely-executed paintings only by exhibiting the actual motions of the objects viewed, men walking, horses trotting, soldiers marching, banners streaming, and foliage shaking in the breeze. THE CAMERA LUCIDA. This ingenious instrument, the invention of Dr. Wollaston, consists of a quadrilateral prism, of which A B C D represents a section made by a plane at right angles to each of its edges, mounted upon an axle parallel to its edges. This axle is attached to the end of a rod sliding in a tube, which has at the other end a clamp for fixing it to the edge of a table, so that the distance of the prism from the table can be shortened or lengthened at pleasure. A B is equal T R B to B C, and AD to D C, and the angles of the prism are a right angle at B, an angle of 135° at D, and angles each 67° 30′ at A and c. Over the face B A, and projecting beyond A, is a plate of metal having in it a narrow longitudinal aperture, which is just bisected by the edge A of the prism. The axis QR, of a small pencil of light from an object q, directly in front of the face BC, passes straight through this face, and falls upon the face D c, making with it an angle of 22° 30'. It is there reflected into the direction Rs, and falling upon the face DA, at the same angle, is again reflected into the direction ST, perpendicular to the face AB, and consequently passes straight through this face without refraction. Looking down through the aperture in the metal plate, an image of the object is seen at P, at a distance from A B equal to the distance of the object itself from в c; and if A в be placed, by means of the sliding rod before mentioned, at a distance from the table equal to the distance of the object from the prism, and a sheet of paper be laid upon the table at P, the apparent place of the object, as seen through the prism, will coincide with the actual place of the paper, seen through the projecting part of the aperture, and an accurate drawing of the object may be traced upon the paper. If the object Q be distant, its image may be brought nearer, and thus made to coincide with the place of the paper, by placing a concave lens before the face BC of the prism. PART III.-SURVEYING INSTRUMENTS. SURVEYING instruments may be divided into three classes: 1. Instruments for measuring distances. 2. Instruments for measuring angles. 3. Instruments for laying down the survey upon paper, or, as it is called, plotting the survey. Under the first of these classes we propose to describe— 1. The chain. 2. The spirit level and levelling staves. * When a ray of light passes from a denser into a rarer medium it is refracted farther from the perpendicular to the refracting surface, so that, if be the angle which the ray in the denser medium makes with the perpendicular to this surface, and o' the angle which the ray in the rarer medium, after refraction, makes with the same perpendicular, sin. sin. ', the refracting power being greater than unity. If, then, the angle be increased, the angle p' is also increased, and becomes a right angle, when 1 = becomes equal to the angle whose sine is equal The ray then is re fracted directly along the surface, and neither emerges, nor is reflected; but, if be still farther increased, the ray of light is reflected back into the denser medium, according to the ordinary law of reflection. With ordinary crown glass, for which 3, this takes place when exceeds 41° 49′, or the ray makes with the surface an angle less than 48° 11'. Under the second we shall include 1. The prismatic compass. 3. The optical square. 2. The box sextant. 4. The theodolite. And under the third, in addition to the instruments already described in Part I. of this Work, we shall say something of— 1. The large circular protractor. 2. The T square and semicircular protractor. 4. The station pointer. THE LAND CHAIN. Gunter's chain is the instrument used almost universally for measuring the distances required in a survey. For extensive and important surveys, however, such as those carried on under the Board of Ordnance, a base of about 5 or 6 miles in length is first measured by some more accurate instrument, and all the principal lines, and the distances of the extreme points, are calculated from triangles connecting them with this base. An instrument which has been known to answer well for this purpose is a steel chain 100 feet long, constructed by Ramsden, jointed like a watch chain. chain is always stretched to the same tension, supported on troughs laid horizontally, and allowances are made for changes in its length made by temperature, at the rate of 0075 of an inch for each degree of heat from 62° of Fahrenheit. This To return, however, to Gunter's chain ;—it is 66 feet, or four poles in length, and is divided into 100 links, which are joined together by rings. The length of each link, together with the 66 × 12 rings connecting it with the next, is consequently inches, or 7.92 inches. To every tenth link are attached pieces of brass of different shapes for more readily counting the links in distances less than a chain. 100 The following tables exhibit the number of chains and links in the different units of lineal measure, and the number of square chains and links in the different units of square measure, made use of in this country : A TABLE OF LINEAR MEASURES. Sq.Mile. 64,000,000 2,787,400 3,097,600 | 102,400 6,400 2,560 640 1 As, then, an acre contains 100,000 square links, if the content of a survey, cast up in square links, be divided by 100,000, the quotient gives at once the content in acres, and decimals of an acre. But the division by 100,000 is performed by merely pointing off the five last figures towards the right hand for the decimals of an acre, and the remaining figures towards the left hand are the acres in the content required. 1175 1175 5875 8225 12925 13.80625 The decimals thus pointed off being then multiplied by 4, and the five last figures pointed off as before, the remaining figures are the roods; and the five decimals cut off from this product, multiplied by 40, give the poles, or perches, and decimals of a pole, the same number, 5, of digits being again pointed off, including the zero, which arises from the multiplication by 40. Thus, if the side of a square field measured 11 chains, 75 links, or 1175 links, the area of the field would contain 1175 × 1175, or 1,380,625 square links, which is equivalent to 13.80625 acres. Then 80625 acres is equivalent to 80625 × 4, or 3·22500 roods; and, again, ·22500 roods is equivalent to 22500 × 40, or 9.00000 poles. The field consequently would measure 13 acres, 3 roods, 9 poles. 4 3.22500 40 9.00000 Ten arrows must be provided with the chain, about 12 inches long, pointed at one end, so as to be easily pressed into the ground, and turned at the other end, so as to form a ring to serve for a handle. In using the chain marks are first to be set up at the extremities of the line to be measured. Two persons are then required to perform the measurement. The chain leader starts with the ten arrows in his left hand, and one end of the chain in his right, while the follower remains at the starting point, and, looking at the mark, or staff, at the other extremity of the line to be measured, directs the leader to extend the |